Welcome to the forum.
Here is small start on answers for you.
The Christmas market in Montreux is one of the best in Switzerland. Good choice.
At your travel times, the Alpine resorts are heavily booked for the Christmas holidays. May already be full.
Hiking may be difficult at high altitudes. Many trails are closed. However, the cableways will be running, after starting up from the autumn break, to service skiers, usually starting about December 15th, although they may run weekends in early December if the snow is good..
Check the time table for a particular day....for example...Grindelwald to First.
Today, the time table only runs into November. it will change over for december and 2017 in the next few days. You'll need to watch for that to check on the cableway to First, for example. Don't know if the trail to Bachalpsee will be open. Some trails are kept clear for hikers....don't know which ones.
Arno and Annika will be able to help with those details.
The cograil to the Jungfraujoch runs every day of the year.
I don't understand your dates for Zermatt.
For the Schilthorn, you may stay in Lauterbrunnen or Wengen, but although it is desirable, it is not absolutely necessary to move from Grindelwald. The one way trip takes about an hour to 1 hour and one half, via Zweilütschinen, so it is a significant time spent on the train, however.